成功大學博碩士論文系統

簡易檢索 / 詳目顯示

回結果列表

研究生：	莊曜宇 Chuang, Yao-Yu
論文名稱：	二維料斗內顆粒流之實驗研究與數值模擬 Experimental Study and Numerical Simulation of Granular Flow in Two-Dimensional Hoppers
指導教授：	楊天祥 Yang, Tian-Shiang
學位類別：	碩士 Master
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2010
畢業學年度：	98
語文別：	中文
論文頁數：	97
中文關鍵詞：	顆粒流、料斗、堵塞、細胞自動機
外文關鍵詞：	granular flow, hopper, jamming, cellular automata
相關次數：	點閱：71 下載：1
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

本文建立一組顆粒流實驗，將相同尺寸的鋼珠，置於二維料斗內，
以重力驅動鋼珠流動。實驗結果指出，當出口寬度大於臨界值時，將不會有堵塞的情事發生；而當鋼珠通過一寬度較小的出口時，鋼珠會形成圓弧結構堵塞於出口處。實驗結果顯示，當料斗出口寬度由小逐漸增大，堵塞機率也從1 遞減至0。
基於顆粒流實驗結果，本研究發展出一套計算模型來模擬顆粒於二
維料斗內的運動行為。該計算模型以類似細胞自動機的簡單算則，來反映顆粒間之複雜碰撞行為，並配合亂數選取來改變顆粒的位置，模擬出顆粒體亂中有序的流動形態。數值模擬結果與實驗結果之比較顯示，本研究所發展的計算模型能呈現出顆粒流的主要特徵，且當料斗外形改變後，也可反應出變化的趨勢。我們期望在未來，可以使用此計算模型來協助降低料斗的堵塞機率。

In this work, gravity-driven granular flow of mono-disperse steel balls in a two-dimensional hopper is studied experimentally and numerically. The experimental results indicate that no jamming would occur if the width of the
hopper opening is larger than a certain threshold width. However, as the hopper opening narrows, the probability for the occurrence of jamming would increase, and become unity when the hopper opening width falls below a critical width. Also, when jamming occurs, an “arch” structure forms at the hopper opening to stop the granular flow.
Based on the experimental results, a computational model also is developed here to simulate the granular flow. Instead of using complex dynamical laws, the model uses simple cellular automata-like decision rules with randomized particle movement (which adds some ordered chaos to the granular flow) to update the particle locations. By properly tuning a number of model parameters―whose specific values appear to be rather robust against variations of the hopper geometry however―the numerical results of the jamming probability compare favorably with the experimental results.
This suggests that the computational model developed in this work indeed can capture the main features of the granular flow, and can be used in future work to help identify strategies that may reduce the hopper jamming probability.

摘要 .................................................................................................................... I
Abstract............................................................................................................. II
致謝 ................................................................................................................. III
目錄 ................................................................................................................. IV
圖目錄 ........................................................................................................... VII
表目錄 ........................................................................................................... XII
符號說明 ...................................................................................................... XIII
第一章 緒論 .................................................................................................. 1
1 顆粒流的應用 .................................................................................. 1
2 研究目的 .......................................................................................... 2
3 文獻回顧 .......................................................................................... 3
3.1 實驗回顧 ............................................................................... 3
3.2 理論回顧 ............................................................................. 10
4 本文架構 ........................................................................................ 18
第二章 二維顆粒流實驗 ............................................................................ 19
1 硬體架構 ........................................................................................ 20
2 實驗流程 ........................................................................................ 22
3 顆粒流動行為概述 ........................................................................ 23
4 實驗結果 ........................................................................................ 25
4.1 參數設定 ............................................................................. 25
4.2 出口寬度與堵塞機率的關係 - I ........................................ 27
4.3 出口寬度與堵塞機率的關係 - II ...................................... 29
4.4 因次分析和參數討論 ......................................................... 31
4.5 堵塞形式與料斗出口寬度的討論 - I ................................ 34
4.6 堵塞形式與料斗出口寬度的討論 - II .............................. 39
第三章 數值計算模型 ................................................................................ 42
1 背景簡介 ........................................................................................ 42
2 計算模型的基本假設 .................................................................... 44
2.1 定義計算區域 ..................................................................... 44
2.2 鋼珠的描述 ......................................................................... 46
2.3 移動方式的假設 ................................................................. 47
2.4 移動順序的假設 ................................................................. 51
3 計算規則與流程圖 ........................................................................ 51
3.1 鋼珠的移動方式 ................................................................. 52
3.2 移動權重的配置與討論 ..................................................... 52
3.3 重疊顆粒之判斷 ................................................................. 55
3.4 數值計算流程 ..................................................................... 57
第四章 結果與討論 .................................................................................... 60
1 實驗結果回顧 ................................................................................ 60
2 各項計算參數設定之討論 ............................................................ 62
2.1 網格大小為2 mm 時計算與實驗結果的差異 .................. 63
2.2 網格大小為1 mm 時計算與實驗模型的差異 .................. 68
2.3 網格大小為0.5 mm 時計算與實驗模型的差異 ............... 72
3 計算模型適用範圍之探討 ............................................................ 76
3.1 鋼珠顆數( N )適用範圍 ...................................................... 76
3.2 儲料區寬度( 1 W)適用範圍 .................................................. 79
4 結果總結 ........................................................................................ 88
5 平行運算對於程式優化之討論 .................................................... 90
5.1 平行運算的適用性與概念 ................................................. 90
5.2 優化前後的比較 ................................................................. 91
第五章 結論與未來研究方向 .................................................................... 93
1 全文歸納 ........................................................................................ 93
2 結果與討論 .................................................................................... 93
3 未來研究方向 ................................................................................ 94
參考文獻 ......................................................................................................... 95
附錄一 ............................................................................................................. 97
                                    

[1] 賈魯強、黎璧賢, "漫談顆粒體物理," 物理雙月刊, Vol.23, No.4, pp.503-510, 2001.
[2] Campbell, C. S., "rapid granular flows," Annual Review of Fluid Mechanics, Vol.22, pp.57-90, 1990.
[3] Jaeger, H. M., Nagel, S. R., and Behringer, R. P., "Granular solids, liquids, and gases," Reviews of Modern Physics, Vol.68, No.4, p.1259, 1996.
[4] To, K., "Gravity driven granular steady state flows in two-dimensional hoppers and silos," Modern Physics Letters B, Vol.19, No.30, pp.1751-1766, 2005.
[5] To, K., Lai, P.-Y., and Pak, H. K., "Flow and jam of granular particles in a two-dimensional hopper," Physica A: Statistical Mechanics and its Applications, Vol.315, No.1-2, pp.174-180, 2002.
[6] To, K. and Lai, P.-Y., "Jamming pattern in a two-dimensional hopper," Physical Review E, Vol.66, No.1, p.011308, 2002.
[7] To, K., Lai, P.-Y., and Pak, H. K., "Jamming of Granular Flow in a Two-Dimensional Hopper," Physical Review Letters, Vol.86, No.1, p.71, 2001.
[8] Zuriguel, I., Pugnaloni, L. A., Garcimartín, A., and Maza, D., "Jamming during the discharge of grains from a silo described as a percolating transition," Physical Review E, Vol.68, No.3, p.030301, 2003.
[9] Zuriguel, I., Garcimartín, A., Maza, D., Pugnaloni, L. A., and Pastor, J. M., "Jamming during the discharge of granular matter from a silo," Physical Review E, Vol.71, No.5, p.051303, 2005.
[10] Mankoc, C., Janda, A., Arévalo, R., Pastor, J., Zuriguel, I., Garcimartín, A., and Maza, D., "The flow rate of granular materials through an orifice," Granular Matter, Vol.9, No.6, pp.407-414, 2007.
[11] Beverloo, W. A., Leniger, H. A., and van de Velde, J., "The flow of granular solids through orifices," Chemical Engineering Science, Vol.15, No.3-4, pp.260-269, 1961.
[12] Janda, A., Zuriguel, I., Garcimartín, A., Pugnaloni, L. A., and Maza, D., "Jamming and critical outlet size in the discharge of a two-dimensional silo," EPL (Europhysics Letters), Vol.84, No.4, p.44002, 2008.
[13] 蔡宏榮，"顆粒流體在粗糙表面之潤滑理論模型的建立與應用"，國立中正大學機械工程學系博士論文，2003。
[14] Lee, H. Y., Lee, H. W., and Kim, D., "Origin of Synchronized Traffic Flow on Highways and Its Dynamic Phase Transitions," Physical Review Letters, Vol.81, No.5, p.1130, 1998.
[15] Lee, H. Y., Lee, H. W., and Kim, D., "Dynamic states of a continuum traffic equation with on-ramp," Physical Review E, Vol.59, No.5, p.5101, 1999.
[16] Haff, P. K., "Grain Flow as a Fluid-Mechanical Phenomenon," J. Fluid Mech., Vol.134, pp.401-430, 1983.
[17] Helbing, D., Farkas, I., and Vicsek, T., "Simulating dynamical features of escape panic," Nature, Vol.407, No.6803, pp.487-490, 2000.
[18] Helbing, D., Buzna, L., Johansson, A., and Werner, T., "Self-Organized
Pedestrian Crowd Dynamics: Experiments, Simulations, and Design Solutions," TRANSPORTATION SCIENCE, Vol.39, No.1, pp.1-24, February 1, 2005, 2005.
[19] Boresi, A. P., Schmidt, R. J., and O.M., S., Advanced Mechanics of Materials, Fifth ed., pp. 692-731 John Wieley & Sons, Inc., 1992.
[20] Timoshenko, S., Strength of Materials, third ed., pp. 339-343 D.Van Nostrand Company,Inc., 1976.
[21] Smith, L., "Monte Carlo simulation of particle behaviour," Metal Powder Report, Vol.56, No.1, pp.32-35, 2001.
[22] Cundall, P. A. and Strack, O. D. L., "A discrete numerical model for granular assemblies.," Géotechnique, Vol.29, No.1, pp.47-65, 1979.
[23] Tsuji, Y., Kawaguchi, T., and Tanaka, T., "Discrete particle simulation of two-dimensional fluidized bed," Powder Technology, Vol.77, No.1, pp.79-87, 1993.
[24]Zuse,K.,Rechnender Raum pp. 336-344 Elektronische Datenverarbeitung, 1967.
[25] Gardner, M., "The fantastic combinations of John Conway's new solitaire game "life'," Scientific American, Vol.223, pp.120-123, 1970.
[26] Schadschneider, A., "Traffic flow: a statistical physics point of view," Physica A: Statistical Mechanics and its Applications, Vol.313, No.1-2, pp.153-187, 2002.
[27] Wolf-Gladrow, D. A., Lattice-gas cellular autimata and lattice Boltzmann models, Springer, 2000.
[28] 孫私于，"應用晶格波茲曼法與場協同理論於流過具障礙物之渠道熱流分析"，國立成功大學機械工程學系碩士論文，2006。
[29] Wolfram, S., A New Kind of Science, Wolfram Media, 2002.
[30] Kozicki, J. and Tejchman, J., "Application of a cellular automaton to simulations of granular flow in silos," Granular Matter, Vol.7, No.1, pp.45-54, 2005.

校內：2013-08-17公開
校外：2020-12-31公開

簡易檢索 / 詳目顯示

相關論文